PYQ Vault

Day 91: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Probability. Asked once: 2022 (same type asked 2 times)

    3
    Three friends A, B and C got their photograph clicked. Find the probability that B is standing at the central position, given that A is standing at the left corner.

  2. Question 2

    Relations and Functions. Asked once: 2026 (same type asked 2 times)

    32 (b)
    A function f:R−{35}⟶R−{35}f : R - \left\{ \frac{3}{5} \right\} \longrightarrow R - \left\{ \frac{3}{5} \right\} is defined as f(x)=3x+25x−3f(x) = \frac{3x + 2}{5x - 3}. Show that f is one-one and onto.

  3. Question 3

    Relations and Functions. Asked once: 2026 (same type asked 2 times)

    32 (a)
    A relation R is defined on Z, the set of integers, as R={(x,y):∣x−y∣ is divisible by a prime number ’p’,x,y∈Z}R = \{(x, y) : \left| x - y \right| \text{ is divisible by a prime number 'p'}, x, y \in Z\} check whether R is an equivalence relation or not.

  4. Question 4

    Three Dimensional Geometry. Asked once: 2023 (same type asked 2 times)

    25 (a)
    Find the vector equation of the line passing through the point (2, 1, 3) and perpendicular to both the lines x−11=y−22=z−33\dfrac{x-1}{1} = \dfrac{y-2}{2} = \dfrac{z-3}{3}; x−3=y2=z5\dfrac{x}{-3} = \dfrac{y}{2} = \dfrac{z}{5}.

  5. Question 5

    Three Dimensional Geometry. Asked once: 2026 (same type asked 2 times)

    17
    Direction ratios of lines l1l_1 and l2l_2 are <12,−3,9><12, -3, 9> and <4,q,−p><4, q, -p> respectively. The values of p and q for which l1l_1 and l2l_2 are parallel are respectively :

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